Use the first derivative test to determine the local extrema of $f ( x ) = ( x - 1 ) ^ { 2 } ( x + 2 )$
A) f has a local maximum at x = 2 and a local minimum at x = 1.
B) f has a local maximum at x = 1 and a local minimum at x = -1.
C) f has a local maximum at x = 1 and has no local minimum.
D) f has a local maximum at x = -1 and a local minimum at x = 1.

Question

Quizplus · Accepted Answer

The first derivative test shows that f'(x) changes from positive to negative at x = -1 (local maximum) and from negative to positive at x = 1 (local minimum).

Use the First Derivative Test to Determine the Local Extrema f(x)=(x−1)2(x+2)f ( x ) = ( x - 1 ) ^ { 2 } ( x + 2 )f(x)=(x−1)2(x+2)

Use the First Derivative Test to Determine the Local Extrema $f ( x ) = ( x - 1 ) ^ { 2 } ( x + 2 )$